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statuscvo [17]
3 years ago
12

An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, t

he altitude cuts the base into two equal segments. The length of the altitude is 21 inches, and the length of the base is 18 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.
*High School Level*
Mathematics
1 answer:
irina1246 [14]3 years ago
3 0

Answer:

63.7 inches

Step-by-step explanation:

half the base is 9 inches, so the equal legs are each

L = √(9² +21²) = 22.8473...

Perimeter  = 2(22.8473) + 18 = 63.6946... ≈ 63.7 inches.

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For the line segment whose endpoints are A(0,0) and B(4, 3), find the x value for the point located
Crank

Answer:

Step-by-step explanation:

The distance between A and B is given by the Pythagorean Theorem:

= \sqrt{(4-0)^{2}+(3-0)^{2}} = 5

The angle of the line segment is:

\theta = \tan^{-1}\left(\frac{3-0}{4-0} \right)\\\\\theta \approx 36.870^{\circ}

The x-coordinate of the point is:

x = 0 + \frac{2}{3}\cdot (5) \cdot \cos 36.870^{\circ}\\\\x = 2.667

x≅ 2.7

6 0
3 years ago
Read 2 more answers
Solve this system using the linear combination method. Show your work.
kipiarov [429]

Answer:

Let's solve for x.

4x+2y=5

Step 1: Add -2y to both sides.

4x+2y+−2y=5+−2y

4x=−2y+5

Step 2: Divide both sides by 4.

4x

4

=

−2y+5

4

x=

−1

2

y+

5

4

Let's solve for x.

−4x−5y=7

Step 1: Add 5y to both sides.

−4x−5y+5y=7+5y

−4x=5y+7

Step 2: Divide both sides by -4.

−4x

−4

=

5y+7

−4

x=

−5

4

y+

−7

4

Answer:

x=

−5

4

y+

−7

4

Step-by-step explanation:

I hope this helps

3 0
3 years ago
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.
grandymaker [24]
(2x+1)^{\cot x}=\exp\left(\ln(2x+1)^{\cot x}\right)=\exp\left(\cot x\ln(2x+1)\right)=\exp\left(\dfrac{\ln(2x+1)}{\tan x}\right)

where \exp(x)\equiv e^x.

By continuity of e^x, you have

\displaystyle\lim_{x\to0^+}\exp\left(\dfrac{\ln(2x+1)}{\tan x}\right)=\exp\left(\lim_{x\to0^+}\dfrac{\ln(2x+1)}{\tan x}\right)

As x\to0^+ in the numerator, you approach \ln1=0; in the denominator, you approach \tan0=0. So you have an indeterminate form \dfrac00. Provided the limit indeed exists, L'Hopital's rule can be used.

\displaystyle\exp\left(\lim_{x\to0^+}\dfrac{\ln(2x+1)}{\tan x}\right)=\exp\left(\lim_{x\to0^+}\dfrac{\frac2{2x+1}}{\sec^2x}\right)

Now the numerator approaches \dfrac21=2, while the denominator approaches \sec^20=1, suggesting the limit above is 2. This means

\displaystyle\lim_{x\to0^+}(2x+1)^{\cot x}=\exp(2)=e^2
7 0
3 years ago
Kevin can travel 22 1/2 miles in 1/3 hour .What is the average speed in miles per hour?
Fantom [35]
You can choose to answer this with fractions or decimals. I'll choose fractions because we won't need calculators. 22 1/2 miles "in" 1/3 hour, means 22 1/2 mi divided by 1/3 hour.
22 1/2 = [(22×2) + 1] ÷ 2 = 45/2
So (45/2)mi ÷ (1/3)hr is the same as (45/2) × (3/1), or (45×3)/2 = 135/2, which is 67 1/2, or 67.5 mi/hr (mph).
8 0
3 years ago
If f(x) = 3x – 2 and g(x) = 2x + 1, find (f + g)(x).
sergey [27]
The answer is 5x^2-x because you have to plug in and then distribute. 
7 0
3 years ago
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